What integers do not occur among the integer coordinated points on surface of 4D radius 85 sphere?
You need the answer to " How many integer coordinated points are on the surface of a four-dimensional sphere of radius 85, given that the center of that sphere is at a integer coordinated point itself? " to work this problem. Do not try this problem if you haven't gotten the answer to the other problem.
This problem's question: What absolute value integers do not occur among the integer coordinated points on surface of 4D radius 85 sphere?
Take the solution set for " How many integer coordinated points are on the surface of a four-dimensional sphere of radius 85, given that the center of that sphere is at a integer coordinated point itself? " (another problem submitted previously), extract a list of all of the integer coordinates (each point contributes four integers to the list), take those values' absolute values, reduce this list (it has duplicates) to a set (i. e., without duplicates). compute the complement of that set against a set of all integers from 0 to 85. That is: find the set of integers that are in which in the range of 0 to 85 and are not in the solution set. That set will be small. sort that small set into ascending order and concatenate the values to assemble another integer. To explain that last step: assume that the answer so far was {29, 37, 41, 63}, then final answer would be 29374163.
The answer is 112935.
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1 solution
If you have done the previous problem, then this problem is relatively easy.
Complement [ Range [ 0 , 8 5 ] , Union [ Flatten [ r ] ] ] ⇒ { 1 1 , 2 9 , 3 5 }
The Flatten function does the extraction of the integer components of the coordinates of the result set. The Union function does the conversion of the list to a set. The Complement function does the complement operation. The value r is the solution set from the original problem.